A New Approach for Solving the Optimal Control Problem of Nonlinear Systems in Control-affine Form

In this paper, a novel practical approach is proposed to solve successfully a class of nonlinear optimal control problems (OCP's). In this approach, the nonlinear two-point boundary value problem (TPBVP) derived from the Pontryagin's maximum principle is transformed into a sequence of nonhomogeneous linear time-invariant TPBVP's. By solving the proposed linear TPBVP sequence in a recursive manner, the optimal control law and the optimal trajectory are determined in terms of uniformly convergent series. A control design algorithm with low computational complexity and fast convergence rate is also presented. Through the finite iterations of the algorithm, a closed-form expression is obtained for the suboptimal control law. Finally, an illustrative example is employed to show the effectiveness of the proposed approach.